TonalityGUIDE - basic tonal music theory and analysis for undergraduates
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Key and Modulation

introduction major and minor the circle of fifths ways of modulating spotting modulations

abrupt modulation | pivot chords | chromatic pivots

Pivot chords
One common way of making the modulation from one key to another smoother is to use a chord that is common to both keys as a sort of pivot. In the example below, the A minor triad (the second chord) is vi in C major and i in A minor.

A pivot chord modulation is only possible if the two keys are closely enough related on the circle of fifths (or by relative or parallel minor) to share a common triad.

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